The Mirror says Swansea are stepping up their interest in Yiadom.
The Ghana international, 26, is out of contract at Oakwell at the end of the season.
He has rejected a new deal and Barnsley are set to cash in on him in January.
The Yorkshire club had originally been asking for £3million for the attacking full-back.
But the Tykes are now willing to drop their price and the Swans have started to negotiate.